Integration

Extending integration to exponentials, logarithms and trig functions, and building the toolkit of techniques — substitution, parts and partial fractions — that turns hard integrals into standard ones. The topic finishes with areas between curves and with solving differential equations to model real situations.

• An Overview — choosing the right method, the notation, and the common mistakes

The content statements

• Standard Integrals — eˣ, 1/x and trig functions, the reverse chain rule, f′(x)/f(x), and integrating with trig identities
• Integration by Substitution — choosing a substitution, replacing dx, and changing the limits of a definite integral
• Integration by Parts — the reverse of the product rule, choosing u, repeated parts and integrating ln x
• Integrating with Partial Fractions — splitting a fraction with linear or repeated linear factors and integrating each piece
• Areas and Integration as a Limit — the integral as the limit of a sum, areas between curves, and areas under parametric curves
• Differential Equations — separating the variables, general and particular solutions, and modelling growth, decay and cooling

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Each page has step-by-step notes, several worked examples, a quick-reference grid and ten practice questions with fully worked solutions.